Finite Group Databasebeta

← #11795373

Subgroups — #11795373

Order 1152.

411 conjugacy classes of subgroups; only the 116 normal subgroups are shown.

normal subgroups only

This group has 411 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×#107C211yesmaximal, characteristic, complemented
2C2×#63380C211yesmaximal, characteristic
3#10588668C211yesmaximal, characteristic
4#10588657C211yesmaximal, characteristic, complemented
5C2×#63369C211yesmaximal, characteristic
6C2×#63367C211yesmaximal, characteristic, complemented
7#10588228C211yesmaximal, characteristic, complemented
8#70640—31nomaximal
9C22×D36C2211yescharacteristic
10C22×C8×C9C2211yescharacteristic
11C2×C9×C4⋊C4C2211yescharacteristic
12C2×C9×C4⋊C4C2211yescharacteristic
13C2×(C2×D9)⋊C4—22no—
14C2×C4⋊Dic9C2211yescharacteristic
15C2×C4×Dic9C2211yescharacteristic
16C22×C9⋊C8C2211yescharacteristic
17C9×#107—22no—
18C9⋊#95—22no—
19#63380—22no—
20#63369—22no—
21#63367—22no—
22C2×C3×#107D311yescharacteristic
23C2×#821—31no—
24#4988—31no—
25#4977—31no—
26C2×#809—31no—
27C2×#808—31no—
28#4550—31no—
29C23×D9—21no—
30C22×C4×C9—21no—
31C22×C4×C9—21no—
32C22×C4×C9C2311yescharacteristic
33C22×Dic9—21no—
34C22×Dic9D412yes—
35C2×D36—21no—
36C2×D36—21no—
37C2×D36—21no—
38C2×D36—21no—
39C2×D36—21no—
40C2×D36Q812yes—
41C2×C8×C9—21no—
42C2×C8×C9—21no—
43C2×C8×C9D412yes—
44C9×C4⋊C4—21no—
45C9×C4⋊C4—21no—
46C9×C4⋊C4—21no—
47C9×C4⋊C4—21no—
48(C2×D9)⋊C4—44no—
49C4⋊Dic9—21no—
50C4⋊Dic9—21no—
51C4×Dic9—21no—
52C4×Dic9—21no—
53C2×C9⋊C8—21no—
54C2×C9⋊C8—21no—
55C2×C9⋊C8D412yes—
56#2092—91noSylow
57C22×D12—31no—
58C22×C3×C8C2×D311yescharacteristic
59C2×C3×C4⋊C4C2×D311yescharacteristic
60C2×C3×C4⋊C4C2×D311yescharacteristic
61C2×(C2×D3)⋊C4—62no—
62C2×C4⋊Dic3—31no—
63C2×C4×Dic3—31no—
64C22×C3⋊C8—31no—
65C3×#107—22no—
66C3⋊#95—62no—
67#821—62no—
68#809—62no—
69#808—62no—
70C23×C9C2×D411yescharacteristic
71C22×D9—22no—
72C22×D9—41no—
73C22×D9—41no—
74C22×D9—42no—
75C22×D9—42no—
76C2×C4×C9—41no—
77C2×C4×C9—41no—
78C2×C4×C9—42no—
79C2×C4×C9—42no—
80C2×C4×C9C2×D411yescharacteristic
81C2×C4×C9C2×D411yescharacteristic
82C2×C4×C9C2×Q811yescharacteristic
83C2×C4×C9#4111yescharacteristic
84C2×C4×C9#4111yescharacteristic
85C2×C4×C9#4111yescharacteristic
86C2×Dic9—22no—
87C2×Dic9—22no—
88C2×Dic9—22no—
89C2×Dic9—41no—
90C2×Dic9—42no—
91D36—22no—
92D36—22no—
93D36—41no—
94D36—41no—
95C8×C9—22no—
96C9⋊C8—22no—
97C2×#107D911yescharacteristic, complemented
98C2×#106—91no—
99C2×#102—91no—
100C2×#102—91no—
101#390—91no—
102#382—91no—
103#336—91no—
104C23×D3—61no—
105C22×C3×C4—21no—
106C22×C3×C4—21no—
107C22×C3×C4C22×D311yescharacteristic
108C22×Dic3—32no—
109C22×Dic3—61no—
110C2×D12—32no—
111C2×D12—61no—
112C2×D12—61no—
113C2×D12—61no—
114C2×D12—61no—
115C2×D12—61no—
116C2×C3×C8—21no—
117C2×C3×C8—21no—
118C2×C3×C8#6712yes—
119C3×C4⋊C4—21no—
120C3×C4⋊C4—21no—
121C3×C4⋊C4—21no—
122C3×C4⋊C4—21no—
123(C2×D3)⋊C4—124no—
124C4⋊Dic3—61no—
125C4⋊Dic3—61no—
126C4×Dic3—61no—
127C4×Dic3—61no—
128C2×C3⋊C8—32no—
129C2×C3⋊C8—61no—
130C2×C3⋊C8—61no—
131C22×C9C22⋊Q811yescharacteristic
132C22×C9#12311yescharacteristic
133C22×C9#12711yescharacteristic
134C22×C9#13512yes—
135C22×C9AGL(1,ℤ/8)12yes—
136C2×D9—42no—
137C2×D9—44no—
138C2×D9—82no—
139C2×D9—81no—
140C2×D9—81no—
141C4×C9—81no—
142C4×C9—81no—
143C4×C9C22⋊Q811yescharacteristic
144C4×C9C22⋊Q811yescharacteristic
145C4×C9#12311yescharacteristic
146C4×C9#12311yescharacteristic
147Dic9—42no—
148Dic9—81no—
149C22×D4—91no—
150C22×C8—91no—
151C22×C8C2×D911yescharacteristic
152C2×C4⋊C4—91no—
153C2×C4⋊C4C2×D911yescharacteristic
154C2×C4⋊C4C2×D911yescharacteristic
155C2×C22⋊C4—182no—
156C2×C42—91no—
157#107—22no—
158#106—182no—
159#102—182no—
160#102—182no—
161#95—182no—
162C23×C3D3×D411yescharacteristic
163C22×D3—62no—
164C22×D3—121no—
165C22×D3—122no—
166C22×D3—122no—
167C22×D3—121no—
168C2×C3×C4—42no—
169C2×C3×C4—42no—
170C2×C3×C4—41no—
171C2×C3×C4—41no—
172C2×C3×C4#23511yescharacteristic
173C2×C3×C4#23511yescharacteristic
174C2×C3×C4D3×D411yescharacteristic
175C2×C3×C4D3×Q811yescharacteristic
176C2×C3×C4#23911yescharacteristic
177C2×C3×C4C2×#6711yescharacteristic
178C2×Dic3—62no—
179C2×Dic3—62no—
180C2×Dic3—62no—
181C2×Dic3—122no—
182C2×Dic3—121no—
183D12—62no—
184D12—62no—
185D12—121no—
186D12—121no—
187C3×C8—22no—
188C3⋊C8—62no—
189C2×C9#39911yescharacteristic
190C2×C9#47812yes—
191C2×C9#48212yes—
192C2×C9#49511yescharacteristic
193C2×C9#49611yescharacteristic
194D9—82no—
195C24—181no—
196C2×D4—92no—
197C2×D4—181no—
198C2×D4—181no—
199C2×D4—181no—
200C2×D4—181no—
201C2×D4—181no—
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—92no—
205C22×C4—181no—
206C22×C4C22×D911yescharacteristic
207C2×C8—21no—
208C2×C8—21no—
209C2×C8—92no—
210C2×C8—181no—
211C2×C8—181no—
212C2×C8#61112yes—
213C4⋊C4—21no—
214C4⋊C4—21no—
215C4⋊C4—21no—
216C4⋊C4—21no—
217C4⋊C4—181no—
218C4⋊C4—181no—
219C22⋊C4—364no—
220C42—181no—
221C42—181no—
222C22×C3#89411yescharacteristic
223C22×C3#89611yescharacteristic
224C22×C3#91112yes—
225C22×C3#91912yes—
226C22×C3#94011yescharacteristic
227C2×D3—124no—
228C2×D3—122no—
229C2×D3—242no—
230C2×D3—241no—
231C2×D3—241no—
232C3×C4—81no—
233C3×C4—81no—
234C3×C4#89411yescharacteristic
235C3×C4#89611yescharacteristic
236C3×C4#92911yescharacteristic
237C3×C4#94611yescharacteristic
238Dic3—122no—
239Dic3—241no—
240C9#209211yescharacteristic, complemented, Sylow
241C23—182no—
242C23—361no—
243C23—361no—
244C23—362no—
245C23—362no—
246C23D4×D911yescharacteristic
247D4—182no—
248D4—182no—
249D4—361no—
250D4—361no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—42no—
254C2×C4—42no—
255C2×C4—182no—
256C2×C4—182no—
257C2×C4—182no—
258C2×C4—361no—
259C2×C4—362no—
260C2×C4#369711yescharacteristic
261C2×C4#369711yescharacteristic
262C2×C4D4×D911yescharacteristic
263C2×C4Q8×D911yescharacteristic
264C2×C4#370111yescharacteristic
265C2×C4C2×#61111yescharacteristic
266C8—22no—
267C8—182no—
268C2×C3#488512yes—
269C2×C3#489112yes—
270C2×C3#499311yescharacteristic
271C2×C3#515411yescharacteristic
272C2×C3#519111yescharacteristic
273D3—242no—
274C22—362no—
275C22—364no—
276C22—722no—
277C22—721no—
278C22—721no—
279C22#6345611yescharacteristic
280C22#6345811yescharacteristic
281C22#6347312yes—
282C22#6348112yes—
283C22#6350211yescharacteristic
284C4—81no—
285C4—81no—
286C4—362no—
287C4—721no—
288C4#6345611yescharacteristic
289C4#6345811yescharacteristic
290C4#6349111yescharacteristic
291C4#6350811yescharacteristic
292C3#7064011yescharacteristic
293C2—722no—
294C2#1058856512yes—
295C2#1058857112yes—
296C2#1058867311yescharacteristic
297C2#1058883411yescharacteristic
298C2#1058887111yescharacteristic
subgroupG/H
centerC23D4×D9
commutator, cosocleC22×C4×C9C23
FrattiniC22×C3×C4C22×D3
FittingC2×C9×#107C2
socleC23×C3D3×D4
prime radicalC22×D36C22
hypercenterC2×#107D9
hypocenterC9#2092
LCSG ▷ C22×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#107

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C9×#107C2semidirect
4. #10588657C2semidirect
6. C2×#63367C2semidirect
7. #10588228C2semidirect
97. C2×#107D9semidirect
240. C9#2092semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C9×#1072
C2×#633802
#105886682
#105886572
C2×#633692
C2×#633672
#105882282
#706403